65.7.2 problem 14.1 (ii)

Internal problem ID [13766]
Book : AN INTRODUCTION TO ORDINARY DIFFERENTIAL EQUATIONS by JAMES C. ROBINSON. Cambridge University Press 2004
Section : Chapter 14, Inhomogeneous second order linear equations. Exercises page 140
Problem number : 14.1 (ii)
Date solved : Tuesday, January 28, 2025 at 06:02:24 AM
CAS classification : [[_2nd_order, _missing_y]]

\begin{align*} x^{\prime \prime }-4 x^{\prime }&=t^{2} \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 26

dsolve(diff(x(t),t$2)-4*diff(x(t),t)=t^2,x(t), singsol=all)
 

\[ x \left (t \right ) = -\frac {t^{2}}{16}-\frac {t^{3}}{12}+\frac {{\mathrm e}^{4 t} c_{1}}{4}-\frac {t}{32}+c_{2} \]

✓ Solution by Mathematica

Time used: 4.008 (sec). Leaf size: 44

DSolve[D[x[t],{t,2}]-4*D[x[t],t]==t^2,x[t],t,IncludeSingularSolutions -> True]
 

\[ x(t)\to \int _1^te^{4 K[2]} \left (c_1+\int _1^{K[2]}e^{-4 K[1]} K[1]^2dK[1]\right )dK[2]+c_2 \]